Thevenin's and Norton's Theorem
Thevenin's Theorem:
Statement:
"Norton’s Theorem states that a linear two-terminal bilateral circuit can be replaced by an equivalent circuit consisting of a current source (IN) and source resistance (RN) connected in parallel. This parallel resistance is called Norton Resistance and it is equal to Thevenin Resistance (RTh)."
Where IN is the short-circuit current through the terminals and RN is the input or equivalent resistance at the terminals when independent sources are inactive or turned off.
Thevenin’s Theorem is used to solve
complicated electrical networks that cannot be solved by conventional methods.
This theorem gives an organized approach to solve the given completed
electrical network. This theorem also gives a technique by
which the fixed part of the network is replaced by an equivalent circuit.
Statement:
"Thevenin’s Theorem states that a
linear two-terminal bilateral circuit can be replaced by an equivalent circuit
consisting of a voltage source (VTh) and source
resistance (RTh) connected in series. This series
resistance is often called Thevenin Resistance."
Where VTh is the open-circuit voltage at the terminals and RTh is the input
or equivalent resistance at the terminals when independent sources are inactive
or turned off.
Inactive sources, Current Sources are
short-circuited and Voltage Sources are open-circuited.
If the given circuit is AC then
the circuit should be transformed to the frequency domain and Impedance (ZTh)
replaces resistance (RTh)
 |
| Figure 1: Thevenin's Theorem |
Conditions/Limitations:
1) Thevenin’s Theorem is not applicable
to the circuits having unilateral elements like a diode etc.
2) Thevenin's Theorem is not applicable
to the circuits that contain magnetic coupling between load and any circuit
element.
3) Thevenin’s Theorem is not applicable
to the circuits that contain nonlinear elements like transistors and diodes
etc.
Steps to solve a given circuit using
Thevenin's Theorem:
(Steps to Thevenize a given circuit)
1. Temporarily remove the load
resistance RL through which current is to calculate.
2. Find the open-circuit
voltage (VOC or Vab or VTh) across the two
terminals a & b from where the load resistance has been removed. That is
your Thevenin's Voltage VTh.
3. Calculate equivalent resistance
between the same two terminals (a & b) by short-circuiting voltage
source and open circuiting current sources (but keeping their internal
resistances). This obtained equivalent resistance is called Thevenin Resistance
(RTh).
4. Now replace the entire network by a
single voltage source VTh and a resistance (RTh) in
series with it.
5. Connect the load
resistance RL back to the terminals a & b from where
it is removed.
6. The obtained circuit is called
Thevenin's Circuit.
7. Now calculate the current flowing
through the load resistance RTh
8. Finally, calculate the current
flowing through the load resistance RL by using Ohms Law:
IL = VTh/ (RTh+RL)
 |
| Figure: 1 a |
Norton’s Theorem:
Edward Lawry Norton (28 July 1898,
Rockland, Maine – 28 January 1983, Chatham, New Jersey) was an engineer and
scientist. He worked at Bell Telephone Laboratory, USA and is known for
Norton's Theorem. In 1926, about 43 years after Thevenin's Theorem, he proposed
a dual of Thevenin's Theorem.
Statement:
"Norton’s Theorem states that a linear two-terminal bilateral circuit can be replaced by an equivalent circuit consisting of a current source (IN) and source resistance (RN) connected in parallel. This parallel resistance is called Norton Resistance and it is equal to Thevenin Resistance (RTh)."
Where IN is the short-circuit current through the terminals and RN is the input or equivalent resistance at the terminals when independent sources are inactive or turned off.
Inactive sources, Current Sources are
short-circuited and Voltage Sources are open-circuited.
If the given circuit is AC then
the circuit should be transformed to the frequency domain and Impedance (ZTh)
replaces resistance (RTh).
Conditions/Limitations:
1) Norton’s Theorem is not applicable
to the circuits having unilateral elements like diode etc.
2) Norton's Theorem is not applicable to the circuits that contain magnetic coupling between load and any circuit element.
2) Norton's Theorem is not applicable to the circuits that contain magnetic coupling between load and any circuit element.
3) Norton’s Theorem is not applicable
to the circuits that contain nonlinear elements like transistors and diodes
etc.
 |
| Figure 2: Norton's Theorem |
Steps to solve a given circuit using Norton's
Theorem:
(Steps to Nortonize a given circuit)
1. Temporarily remove the load resistance RL (from a & b) through
which current is to calculate and put short-circuit across them.
2. Find the short-circuit current Isc.
3. Calculate equivalent resistance between the same
two terminals (a & b) by the short-circuiting voltage source and open
circuiting current sources (but keeping their internal resistances). This
obtained equivalent resistance is called Norton Resistance (RN =
RTh).
4. Now replace the entire network by a single
current source IN and a resistance (RN) in
parallel with it.
5. Connect the load resistance RL back
to the terminals a & b from where it is removed.
6. The obtained circuit is called Norton's Circuit.
7. Finally, calculate the current flowing
through the load resistance RL by using Current Division
Rule:
IL = IN [RN
/ (RN+RL)]
Bilateral Network:
 |
| Figure: 2-a |
Bilateral Network:
A circuit whose characteristic or behavior is same irrespective of the direction of current through various elements of it is called a bilateral network.
A network consisting of only resistances is an example of a bilateral network.
Linear Network:
A linear circuit is an electric circuit in which circuit parameters (Resistance, inductance, capacitance, waveform, frequency, etc) are constant.
In other words, a circuit whose parameters are not changed with respect to Current and Voltage is called Linear Circuit.
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